Program Explanation Given information: The temperature of the cake initially is 210 ° C and the room temperature is 70 ° C . The another condition is the temperature of the cake is 100 ° C after 30 minute. Calculation: Consider the standard equation of Newton’s law of cooling as follows, d T d t = − k ( T − A ) Here, A is the temperature of the outside. The room temperature is 70 ° C therefore, the value of A = 70 . Separate the variables of the above differential equations, as follows: d T ( T − 70 ) = − k d t Integrate the equation on both the sides. ∫ d T ( T − 70 ) = − ∫ k d t Evaluate the above integral as follows, ln c ( T − 70 ) = − k t Further evaluate the above equation for the value of T , as follows: T = 70 + c e − k t ........ (1) Apply the initial condition that the temperature of cake is 210 ∘ F at t = 0 to obtain the value of c . T = 70 + c e − k t 210 = 70 + c e − k ( 0 ) 140 = c c = 140 Now substitute 140 for c in equation (1) to obtain the temperature function. T = 70 + 140 e − k t ........ (2) Apply the boundary condition that temperate of the cake is 140 ∘ F at t = 30 to obtain the value of k

5th Edition

ISBN: 8220100802454

Author: Calvis

Publisher: PEARSON

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Linear Programming Concepts

Linear programming is a famous mathematical modeling tool for determining the best distribution of scarce resources among competing demands. Machinery, time, personnel, raw materials, money, and space are all resources. It is used to find the most optima…

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Chapter 1.4, Problem 67P

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Program Description: Purpose of the problem is to find the time at which the temperature of the cake is 100°F .

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Chapter 1.4, Problem 66P

Chapter 1.4, Problem 68P

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Chapter 1 Solutions

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Program Description: Purpose of the problem is to find the time at which the temperature of the cake is 100 ° F .

Solution Summary: The author explains that the problem is to find the time at which the temperature of the cake is 100°F.

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Program Description: Purpose of the problem is to find the time at which the temperature of the cake is 100°F .

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Chapter 1 Solutions